Renormalized and entropy solutions for the fractional p-Laplacian parabolic equation with L^1 data

TL;DR

This paper introduces a new function class and proves existence, uniqueness, and equivalence of renormalized and entropy solutions for a fractional p-Laplacian parabolic equation with L^1 data, advancing the mathematical understanding of such problems.

Contribution

It establishes the existence, uniqueness, and equivalence of solutions for the fractional p-Laplacian parabolic problem with L^1 data, using a novel function class.

Findings

Existence and uniqueness of solutions are proven.

Renormalized and entropy solutions are shown to be equivalent.

A comparison principle for solutions is established.

Abstract

In this paper we introduce a natural function class and prove the existence and uniqueness of both nonnegative renormalized solutions and entropy solutions for the fractional p-Laplacian parabolic problem with L^1 data. And moreover, we obtain the equivalence of renormalized solutions and entropy solutions and establish a comparison result.